First- and second-order necessary conditions with respect to components for discrete optimal control problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:364

Article

Mardanov, Misir J.¹  Melikov, Telman K.^1,2  Malik, Samin T.³  Malikov, Kamran⁴ 

[1] Inst Math & Mech ANAS, Baku, Azerbaijan

[2] Inst Control Syst ANAS, Baku, Azerbaijan

[3] Azerbaijan Inst Math & Mech ANAS, Baku Higher Oil Sch, Baku, Azerbaijan

[4] Univ Essex, Colchester, Essex, England

关键词: Discrete maximum principle with respect to components;    Singular and quasi-singular controls with respect to components;    Optimal control;    Necessary conditions;    Second-order optimality conditions;   

DOI  :  10.1016/j.cam.2019.112342

来源: Elsevier

【 摘 要 】

This paper is devoted to the study of discrete optimal control problems. We aim to obtain more constructive optimality conditions under weakened convexity assumptions. Based on a new approach introduced in this work, an optimality condition with respect to every component is obtained in the form of a global maximum principle. In addition, an optimality condition with respect to one of the components of a control in the form of the global maximum principle and with respect to another component of a control in the form of the linearized maximum principle are obtained. Furthermore, various second-order optimality conditions in terms of singular and quasi-singular controls with respect to the components are obtained on the fly. (C) 2019 Published by Elsevier B.V.

【 授权许可】

Free